%0 Journal Article
%T On Horn Matrix Function <i>H<sub>2</sub>(A,A¡ä,B,B¡ä;C;z,w)</i> of Two Complex Variables under Differential Operator
%A Mohamed Saleh Metwally
%A Mahmoud Tawfik Mohamed
%A Ayman Shehata
%J Advances in Linear Algebra & Matrix Theory
%P 96-110
%@ 2165-3348
%D 2018
%I Scientific Research Publishing
%R 10.4236/alamt.2018.82009
%X The aim of this paper deals with the study of the Horn matrix function of two complex variables. The convergent properties, an integral representation of <span style=\"white-space:nowrap;\"><i></i></span><i>H<sub>2</sub>(A,A¡ä,B,B¡ä;C;z,w)<span style=\"white-space:nowrap;\"></span></i> is obtained and recurrence matrix relations are given. Some result when operating on Horn matrix function with the differential operator <i>D</i> and a solution of certain partial differential equations are established. The Hadamard product of two Horn¡¯s matrix functions is studied, certain results as, the domain of regularity, contiguous functional relations and operating with the differential operator <i>D</i> and <i>D</i><sup>2</sup> are established.
%K Hypergeometric Matrix Function
%K Horn Matrix Function
%K Integral Form
%K Recurrence Matrix Relation
%K Matrix Differential Equation
%K Differential Operator
%K Hadamard Product
%U http://www.scirp.org/journal/PaperInformation.aspx?PaperID=85481